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A Molecular Dynamics-Based Model for Knudsen Number and Slip Velocity

[+] Author Affiliations
Mohamad I. Cheikh, Emma A. Schinstock, Grant P. Ferland, James Chen

Kansas State University, Manhattan, KS

Paper No. FEDSM2017-69136, pp. V01CT23A003; 7 pages
  • ASME 2017 Fluids Engineering Division Summer Meeting
  • Volume 1C, Symposia: Gas-Liquid Two-Phase Flows; Gas and Liquid-Solid Two-Phase Flows; Numerical Methods for Multiphase Flow; Turbulent Flows: Issues and Perspectives; Flow Applications in Aerospace; Fluid Power; Bio-Inspired Fluid Mechanics; Flow Manipulation and Active Control; Fundamental Issues and Perspectives in Fluid Mechanics; Transport Phenomena in Energy Conversion From Clean and Sustainable Resources; Transport Phenomena in Materials Processing and Manufacturing Processes
  • Waikoloa, Hawaii, USA, July 30–August 3, 2017
  • Conference Sponsors: Fluids Engineering Division
  • ISBN: 978-0-7918-5806-6
  • Copyright © 2017 by ASME


Much research has been devoted to incestigating the relationship between Knudsen number and slip velocity using different lattice Boltzmann methods. However, these models are complex to implement for simulations in continuum regime, and have shown to diverge when compared with Direct Simulation Monte Carlo (DSMC) simulations at high Knudsen numbers. In this study, a molecular dynamics (MD)-based Knudsen number is presented, and the relationship between Knudsen number and slip velocity is presented. The proposed slip model directly correlates the Knudsen number with the slip velocity. The model is implemented on a shear-driven MD simulation of a Couette flow, and curve fitting is used to get an exponential solution for the slip velocity. The solution obtained from the proposed model as well as the solutions from the literature are compared with a DSMC simulation. The results show that the proposed exponential solution agrees well with DSMC simulations in comparison with the models from the literature. The exponential solution can serve as boundary conditions for simulating flows at different Knudsen numbers in continuum regime.

Copyright © 2017 by ASME



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